Analysis of the objective space in multiple objective linear programming (Q1095043)

A multiple objective linear program is defined by a matrix C consisting of the coefficients of the linear objectives and a convex polytope X defined by the linear constraints. An analysis of the objective space \(Y=C[X]\) for this problem is presented. A characterization between a face of Y and the corresponding faces of X is obtained. This result gives a necessary and sufficient condition for a face to be efficient. The theory and examples demonstrate the collapsing (simplification) that occurs in mapping X to Y. These results form a basis for a new approach to analyzing multiple objective linear programs.